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arXiv 2106.15946hep-thcond-mat.stat-mechquant-ph
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Wess-Zumino-Witten模型中对称分辨的纠缠熵

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

Pasquale Calabrese, Jérôme Dubail, Sara Murciano

摘要:

通过对Wess-Zumino-Witten(WZW)模型的深入分析,研究了非阿贝尔对称性下Rényi纠缠熵的分解问题.我们首先考虑$SU(2)_k$作为一个案例研究,然后推广到任意的非阿贝尔李群。我们发现,在领导秩序的子系统大小$L$的纠缠是均匀分布在不同的部门标记的不可约表示的相关代数。我们还确定了打破这种均分的主导项:它不依赖于$L$,但只对尺寸的表示。此外,$\log\log L$对雷尼熵的贡献表现出与模型的基本对称群(即李群的维数)相关的普适形式。

英文摘要:

We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log\log L$ contribution to the Rényi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.

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